I also work in a large city, New York, where I've been mistaken for a Jewess, but not a Muslim as I do not wear a head covering in warm weather, and in cold, my hat would not be worn by a Muslim. Really, it doesn't bother me. Orthodox Jewish women are known for being modest and having good taste in clothing. If necessary, I politely inform the person that I'm Catholic. I don't care what the general public thinks of my clothing because my aim is to please Jesus and Mary. Plus, I'm too busy to go into a long explanation most of the time. In New York, one can pretty much wear anything or nothing(!) without generating undue attention. The only time clothing generates attention is if it obstructs traffic in the street, sidewalk, or on public transportation, or the wearer smells bad. Since I do not cause these problems, I'm usually ignored.
Example, a woman in a huge paper mache bumble bee costume boarded the 6 train during evening rush hour. The stinger poked people and she took up too much room. She was the worthy recipient of obscene remarks before disembarking after a dozen stops. A nude man except for Adidas and a floor buffer ran down the middle of 2nd Avenue at 9:30 pm. He was yelling something about Obama and darting in front of cars. Horns blared, curses were called, and middle fingers raised. As soon as he left the roadway for the relatively vacant sidewalk, there was no more problem.
The OP might consider moving to NY where her modesty will go largely unnoticed!